What distinguishes the sample standard deviation formula from the population version?
Correct Answer
D) The sample version divides by one less than the count
Why this is correct: The sample standard deviation formula uses (n - 1) in the denominator, known as Bessel's correction, while the population formula uses N. This correction accounts for the fact that a sample mean is used to calculate deviations, which tends to underestimate the true population variance. Using n-1 provides an unbiased estimate of the population variance from a sample. Why the other choices are wrong: "The sample version omits the squaring of deviations" is false; both formulas square deviations to calculate variance. "The sample version uses the median instead of a mean" is incorrect; standard deviation is based on the mean. "The sample version discards the highest observation" is not a characteristic of the standard deviation formula. Exam tip: Remember "n-1 for sample." This is a key distinction in inferential statistics that appraisers use when working with market data samples.
Why This Is the Correct Answer
Why this is correct: The sample standard deviation formula uses (n - 1) in the denominator, known as Bessel's correction, while the population formula uses N. This correction accounts for the fact that a sample mean is used to calculate deviations, which tends to underestimate the true population variance. Using n-1 provides an unbiased estimate of the population variance from a sample. Why the other choices are wrong: "The sample version omits the squaring of deviations" is false; both formulas square deviations to calculate variance. "The sample version uses the median instead of a mean" is incorrect; standard deviation is based on the mean. "The sample version discards the highest observation" is not a characteristic of the standard deviation formula. Exam tip: Remember "n-1 for sample." This is a key distinction in inferential statistics that appraisers use when working with market data samples.
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